A Time-Stepping DRBEM for 3D Anisotropic Functionally Graded Piezoelectric Structures Under the Influence of Gravitational Waves Mohamed Abdelsabour Fahmy 1,2(&) 1 Faculty of Computers and Informatics, Suez Canal University, New Campus, 4.5 Km, Ring Road, El Salam District, Ismailia 41522, Egypt mohamed_fahmy@ci.suez.edu.eg, maselim@uqu.edu.sa 2 Jummum University College, Umm Al-Qura University, Jummum, Mecca 21955, Saudi Arabia Abstract. A three-dimensional time-stepping dual reciprocity boundary ele- ment method (DRBEM) modelling was investigated for anisotropic functionally graded piezoelectric Structure (FGPS) under the influence of gravitational waves. The FGPS is assumed to be graded through the thickness. The basic aim of this paper is to describe anisotropic displacement behaviour of the homo- geneous piezoelectric structures (HPS) and FGPS under the influence of Gravitational waves. The accuracy of the proposed method was examined and confirmed by comparing the obtained results with those known previously. Understanding the behaviour of anisotropic FGPS under the effect of gravita- tional waves is the key to extending the application of these structures. Nomenclature x Field point n Load point t Time r Euclidean distance m Dimensionless constant G Gravitational acceleration q Density U Electric potential u h Displacement components r fg Mechanical stress tensor e hi Mechanical strain tensor E i Electric field vector C fghi Elasticity tensor e fhi Piezoelectric tensor ǫ fi Permittivity tensor D Electric displacement © Springer International Publishing AG 2018 H. Rodrigues et al. (eds.), Facing the Challenges in Structural Engineering, Sustainable Civil Infrastructures, DOI 10.1007/978-3-319-61914-9_27